Pythagorean Review

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It is expressed as: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

What is the formula for finding the hypotenuse in a right triangle?

Back

The formula for finding the hypotenuse (c) in a right triangle is: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

If one side of a right triangle is 3 units and the other side is 4 units, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5 units.

Tags

CCSS.8.G.B.7

Front

What is the distance formula used for finding the distance between two points (x1, y1) and (x2, y2)?

Back

The distance formula is: d = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

In a right triangle, if the lengths of the legs are 5 and 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 5² + 12² = c²; 25 + 144 = c²; 169 = c²; c = 13.

Tags

CCSS.8.G.B.7

Front

What does it mean for a triangle to be a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Tags

CCSS.4.G.A.2

Front

If the hypotenuse of a right triangle is 10 and one leg is 6, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 6² + b² = 10²; 36 + b² = 100; b² = 64; b = 8.

Tags

CCSS.8.G.B.7

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Tags

CCSS.HSG.CO.C.10

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Tags

CCSS.8.G.B.8

Front

How do you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if a² + b² = c² holds true for the lengths of the sides.

Tags

CCSS.8.G.B.8